Type Ia supernovae (SNe Ia) in the nearby Hubble flow are excellent distance indicators in cosmology. The Zwicky Transient Facility (ZTF) has observed a large sample of SNe from an untargeted, rolling survey, reaching 20.8, 20.6, and 20.3 mag in g r, and i band, respectively. With an FoV of 47 deg^2^, ZTF discovered > 3000 SNe Ia in a little over 2.5 yr. Here, we report on the sample of 761 spectroscopically classified SNe Ia from the first year of operations (DR1). The sample has a median redshift z_med_ = 0.057, nearly a factor of 2 higher than the current low-z sample. Our sample has a total of 934 spectra, of which 632 were obtained with the robotic SEDm on Palomar P60. We assess the potential for precision cosmology for a total of 305 SNe with redshifts from host galaxy spectra. The sample is already comparable in size to the entire combined literature low-z anchor sample. The median first detection is 13.5 d before maximum light, about 10 d earlier than the median in the literature. Furthermore, six SNe from our sample are at D_L_ < 80 Mpc, for which host galaxy distances can be obtained in the JWST era, such that we have calibrator and Hubble flow SNe observed with the same instrument. In the entire duration of ZTF-I, we have observed nearly 50 SNe for which we can obtain calibrator distances, key for per cent level distance scale measurements.